After unsuccesful spells at Newcastle and Ipswich, Appleby joined the Swans where he played around 150 games in 5 years. He was then taken to Kiddy in November, scoring 4 goals in 20 appearances. His contract runs out this summer, and a new deal is on the table from the Harriers.
Molby said: "Richie Appleby is a player I have a lot of respect and admiration for. He has to be the best midfielder in the Third Division and I would love to bring him here."
Colin Larkin has also been shortlisted as a possible signing. The Wolves attacker played 35 games on loan for Kidderminster last season, scoring 7 goals. Larkin - who will be 20 on Saturday - has represented Ireland at Under-18 level previously.
Molby said: "Colin did really well for me at Kidderminster. He's got a lot of pace, he's very skilful and there aren't too many players like him around at this level of the game. He is under contract at Wolves but I will be speaking to them to see what the situation is.
"They are in the play-offs at the moment so Dave Jones has enough on his plate but hopefully we'll be able to sort something out."
Meanwhile, there are also rumours linking City with Darlington defender Craig Liddle. The 30-year-old former Middlesbrough player is out of contract at Feethams.